CN107622148A - Characteristics of conformal array antenna structure best elasticity mould method for determination of amount based on mechanical-electric coupling - Google Patents
Characteristics of conformal array antenna structure best elasticity mould method for determination of amount based on mechanical-electric coupling Download PDFInfo
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Abstract
The invention discloses a kind of characteristics of conformal array antenna structure best elasticity mould method for determination of amount based on mechanical-electric coupling, including：Determine the structural parameters and electromagnetic parameter of antenna；Provide the modulus of elasticity of initial antenna structure；Deformation under load analysis is carried out to antenna using ANSYS；Calculate the new position of array element after deforming；Establish array element rectangular coordinate system and spherical coordinate system；Determine the transition matrix between array element rectangular coordinate system and spherical coordinate system；Obtain the array element directional diagram under array element rectangular coordinate system；Determine array element rectangular coordinate system and transition matrix；Obtain the array element directional diagram under array rectangular coordinate system；Determine array element excitation amplitude and phase；Calculate space quadrature of each array element at target；Calculate the antenna electric performance parameter after deformation；Judge whether the antenna electric performance parameter under the conditions of the modulus of elasticity meets to require.The present invention effectively determines the best elasticity modulus of characteristics of conformal array antenna structure, so as to instruct the structure design of characteristics of conformal array antenna.
Description
Technical Field
The invention belongs to the technical field of radar antennas, and particularly relates to a method for determining the optimal elastic modulus of a cylindrical conformal array antenna structure based on electromechanical coupling, which can effectively solve the problem of quickly determining the elastic modulus of the cylindrical conformal array antenna structure, so as to guide the structural design of the cylindrical conformal array antenna.
Background
The conformal array antenna is an antenna which keeps consistent with the shape of an object, has the advantages of saving the structural space of a carrier, not influencing the aerodynamic performance of the carrier, reducing the scattering sectional area of a radar and the like, and is widely applied to the field of aerospace, wherein the cylindrical conformal array antenna is the most common conformal antenna form and is widely applied to various radar systems.
With the development of world military technology, the tactical and technical index requirements of the conformal array antenna are higher and higher, wherein the electrical properties of the conformal antenna, such as aperture, gain, side lobe level, beam pointing direction, and the like, have a close relationship with the antenna, and the performance of the conformal array antenna is determined to a great extent. The development trend of the cylindrical conformal array antenna is not only to reduce the weight of the antenna, but also to maintain sufficient strength and rigidity so as to ensure that the cylindrical conformal array antenna can adapt to various loading environments, so that the electrical performance of the cylindrical conformal array antenna under the action of a load meets requirements, and the manufacture, the transportation and the erection of the antenna are convenient. In order to ensure that the cylindrical conformal array antenna has the required antenna performance and works safely, excellent structural design must be performed on the cylindrical conformal array antenna. Therefore, it is necessary to select a suitable material, a structural form of the cylindrical conformal array antenna, and dimensions of each part of the antenna so that the mechanical property and the electromagnetic property of the cylindrical conformal array antenna are satisfied.
At present, a great deal of research is carried out at home and abroad, the influence of different structural parameters on the radiation performance of the antenna is researched, how to select the parameters is also researched, the influence of the structural deformation of the antenna array surface on the radiation performance of the antenna is analyzed, and finally, the structural optimization design is carried out on the antenna according to the performance indexes such as antenna gain, side lobe level and the like. The method well analyzes the influence of the structural parameters on the electrical property of the antenna, optimally designs the structure by taking the electrical property of the antenna as an index, but does not consider the actual load condition of the antenna, and does not consider how to optimize the structural parameters of the antenna when the electrical property of the antenna does not meet the requirements under the action of the actual load. At present, in order to meet the radiation performance of the antenna, optimization is performed on the thickness, the material and the structural form of a carrier layer of the antenna, most of the optimization is performed under ideal conditions, and the actual load environment of the antenna is not considered.
Therefore, it is necessary to study the coupling relationship between the cylindrical conformal array antenna structure and the electromagnetic wave to determine the optimal elastic modulus of the cylindrical conformal array antenna structure effectively, and ensure that the electrical performance of the cylindrical conformal array antenna meets the requirements under the loading environment.
Disclosure of Invention
In order to solve the above-mentioned drawbacks in the prior art, an object of the present invention is to provide a method for determining an optimal elastic modulus of a cylindrical conformal array antenna structure based on electromechanical coupling, which effectively determines the optimal elastic modulus of the cylindrical conformal array antenna structure, so as to guide the structural design of the cylindrical conformal array antenna.
The invention is realized by the following technical scheme.
A method for determining an optimal elastic modulus of a cylindrical conformal array antenna structure based on electromechanical coupling comprises the following steps:
(1) Determining structural parameters and electromagnetic parameters of the cylindrical conformal array antenna according to the initial structural design scheme of the cylindrical conformal array antenna;
(2) The elastic modulus of an initial cylindrical conformal array antenna structure is given;
(3) According to the antenna load environment, performing load deformation analysis on the cylindrical conformal array antenna by using mechanical analysis software ANSYS;
(4) Based on the result of structural load deformation analysis of the cylindrical conformal array antenna, obtaining the circumferential and axial position offset of each array element, and solving the new position of the deformed array element;
(5) According to the new position of the deformed array element, establishing an array element rectangular coordinate system and an array element spherical coordinate system;
(6) Determining a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system;
(7) Based on an array element directional diagram under an array element spherical coordinate system, a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system is utilized to obtain the array element directional diagram under the array element rectangular coordinate system;
(8) Determining a conversion matrix of the rectangular coordinate system of the array elements and the rectangular coordinate system of the array according to the new positions of the deformed array elements;
(9) Based on the array element directional diagram under the array element rectangular coordinate system, the array element directional diagram under the array element rectangular coordinate system is solved by utilizing the conversion matrix of the array element rectangular coordinate system and the array rectangular coordinate system;
(10) Determining array element excitation amplitude and phase according to the orofacial weighted distribution;
(11) Calculating the spatial phase difference of each array element at the target position by combining the position of the phase reference point of the cylindrical conformal array antenna and the new position of the deformed array element;
(12) Calculating a directional diagram of the cylindrical conformal array antenna under the load by utilizing an electromechanical coupling model of the cylindrical conformal array antenna; calculating electrical property parameters of the antenna according to a directional diagram of the cylindrical conformal array antenna, and analyzing the deterioration degree of the electrical property relative to the design index of the cylindrical conformal array antenna;
(13) Judging whether the electrical property of the cylindrical conformal array antenna under the elastic modulus condition meets the requirement or not according to the design index requirement of the cylindrical conformal array antenna, wherein if the electrical property meets the requirement, the current elastic modulus is the optimal parameter of the cylindrical conformal array antenna structure; otherwise, increasing the elastic modulus, and repeating the steps (2) to (12) until the electrical performance of the cylindrical conformal array antenna meets the requirement.
Further, the step (1) of determining the structural parameters and the electromagnetic parameters of the cylindrical conformal array antenna comprises the following steps:
(1a) Determining the cylinder radius r of the cylinder conformal array antenna, the circumferential row number M and the axial column number N of the array elements in the array, the circumferential central angle gamma and the axial distance d of the adjacent array elements z And the structural parameters and the working frequency f of the array elements;
(1b) And numbering array elements in the array surface into (M, N) according to the sequence of circumferential rows and axial columns, wherein M is an integer between 1 and M and represents the number of the Mth row of array elements of the cylindrical conformal array antenna, and N is an integer between 1 and N and represents the number of the Nth column of array elements of the cylindrical conformal array antenna.
Further, the step (4) of obtaining the circumferential and axial position offset of each array element based on the result of the structural load deformation analysis performed by the cylindrical conformal array antenna, and solving a new position of the deformed array element includes the following steps:
(4a) Obtaining the circumferential position offset delta d of each array element according to the result of the load deformation analysis of the cylindrical conformal array antenna structure in the step (3) mn And the amount of axial position deviation Δ z mn 。
(4b) Setting the design coordinates of (m, n) array elements in the array as (x) mn ,y mn ,z mn ) The included angle between the local external normal direction of the array element and the x axis is gamma mn Wherein x is mn ＝r·cosγ mn ，y mn ＝r·sinγ mn And then, the following steps are known:
wherein r is the radius of the cylinder;
(4c) Combined with circumferential position offset deltad of array element mn And the amount of axial position deviation Δ z mn Circumferential arc length Δ d mn Corresponding to a central angle ofThe new position (x ') of the deformed array element can be known' mn ,y′ mn ,z′ mn )：
Further, the establishing of the rectangular array element coordinate system and the spherical array element coordinate system in the step (5) according to the new position of the deformed array element includes the following steps:
(5a) Establishing a rectangular coordinate system of the array elements according to the new positions of the deformed array elementsO′ mn Is the phase center of the (m, n) th array element after deformation,the positive direction of the axis is the local external normal direction of the curved surface placed by the array element after deformation,the axis is in the same direction as the z-axis,tangent to the plane of the antenna element;
(5b) According to the established rectangular array element coordinate system, an array element spherical coordinate system is establishedWhereinPositive direction is O mn ' a vector pointing to any point,the far field direction of the deformed array element coordinate system is shown;in the positive direction ofThe shaft looking straight downThe shaft being rotated anticlockwise to the sagittal diameterThe tangential direction of the projection of the surface,in the positive direction ofThe shaft rotates clockwise to the tangent of the sagittal diameter.
Further, the determining the conversion matrix between the rectangular array element coordinate system and the spherical array element coordinate system in the step (6) includes the following steps:
according to the transformation relation between the spherical coordinate system and the rectangular coordinate system, the array element spherical coordinate system can be obtainedDirection vector to array element rectangular coordinate systemThe transformation matrix of (2):
in the formula (I), the compound is shown in the specification,the matrix is a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system.
Further, the calculating of the array element directional diagram in the array rectangular coordinate system in the step (7) includes the following steps:
(7a) According to the array element structure parameters, the directional diagram of the deformed array element under the array element spherical coordinate system can be obtained:
in the formula (I), the compound is shown in the specification,andin an array element spherical coordinate system for an array element directional diagramAnda component of direction;
(7b) Combined array element spherical coordinate systemAnd array element rectangular coordinate system direction vectorOf the conversion matrixAnd the deformed array element directional diagram under the array element spherical coordinate system can obtain the array element directional diagram under the array element rectangular coordinate system:
in the formula (I), the compound is shown in the specification,andarray element rectangular coordinate system respectively for array element directional diagramAnda component of direction.
Further, the determining a conversion matrix of the rectangular coordinate system of the array elements and the rectangular coordinate system of the array elements according to the new positions of the deformed array elements in the step (8) includes the following steps:
according to the new position of the deformed array element, a conversion matrix from the rectangular array element coordinate system to the rectangular array coordinate system can be determined:
in the formula (I), the compound is shown in the specification,and converting the deformed array element rectangular coordinate system into an array rectangular coordinate system.
Further, the step (9) of obtaining the array element direction diagram in the array rectangular coordinate system by using the conversion matrix of the array element rectangular coordinate system and the array rectangular coordinate system based on the array element direction diagram in the array element rectangular coordinate system includes the following steps:
(9a) Converting matrix T 'from transformed array element rectangular coordinate system to array rectangular coordinate system' eta (Δd mn ) Obtaining far field direction of the deformed array element coordinate systemThe relation between the far field direction (theta, phi) and the array coordinate system;
one point in the far field is represented in the rectangular array coordinate system as:
x＝R sinθcosφ
y＝R sinθsinφ
z＝R cosθ
the point is expressed as follows in a rectangular array element coordinate system:
distance from point in far field to origin of local coordinate system of array elementEqual to its distance R from the origin of the array coordinate system, so there are:
thereby can obtainDetermining the far field directions (theta, phi) in the array coordinate system and the far field directions in the array element coordinate systemThe relationship between;
(9b) Combining the array element directional diagram under the array element rectangular coordinate system, and converting matrix T 'from the deformed array element rectangular coordinate system to the array rectangular coordinate system' eta (Δd mn ) And obtaining an array element directional diagram of the deformed array elements under the array rectangular coordinate system:
in the formula, f mnx (θ,φ,Δd mn )、f mny (θ,φ,Δd mn ) And f mnz (θ,φ,Δd mn ) The components of the deformed array element direction diagram in the three directions of an array rectangular coordinate system x, y and z are respectively; t' eta (Δd mn ) The transformation matrix is a transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;the unit vectors are respectively in three directions of an array rectangular coordinate system x, y and z.
Further, the step (11) of calculating the spatial phase difference of each array element at the target by combining the position of the phase reference point of the cylindrical conformal array antenna and the new position of the deformed array element includes the following steps:
(11a) Unit vector of phase reference point O to any point P (x, y, z) direction of far field
In the formula (I), the compound is shown in the specification,the unit vectors are respectively in three directions of an array rectangular coordinate system x, y and z.
(11b) From the new position of the (m, n) -th array element after the transformation, the unit vector of the (m, n) -th array element relative to the origin O of the coordinate system can be obtained:
wherein r is the radius of the cylinder; gamma ray mn Is the included angle between the local external normal direction of the array element and the x axis; Δ d mn The circumferential position offset of the array element is taken as the offset; Δ z mn The axial position offset of the array element is taken as the axial position offset of the array element;
(11c) The space phase difference of the deformed array elements at the target position is as follows:
in the formula (I), the compound is shown in the specification,is a unit vector of the direction from the phase reference point O to any point P (x, y, z) in the far field,the unit vector of the position of the array element after deformation relative to the origin O of the coordinate system; r is the radius of the cylinder; (x) mn ,y mn ,z mn ) And designing coordinates for the array elements.
Further, in the step (12), a directional diagram of the cylindrical conformal array antenna under the load action is calculated by using an electromechanical coupling model of the cylindrical conformal array antenna; according to the directional diagram of the cylindrical conformal array antenna, calculating the electrical performance parameters of the antenna, and analyzing the deterioration degree of the electrical performance relative to the design index of the cylindrical conformal array antenna, the method comprises the following steps:
(12a) Calculating a directional diagram of the deformed cylindrical conformal array antenna by using the cylindrical conformal array antenna electric coupling model:
in the formula:
I mn for the purpose of its energizing of the current,respectively the amplitude and the phase of the exciting current;
a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system is formed;
T′ eta (Δd mn ) A transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;
the directional diagrams of the deformed array elements under the rectangular coordinate systems of the array elements are the same;
the spatial phase difference of the deformed array elements at the target can be expressed as:r is the radius of the cylinder; gamma ray mn The included angle between the local external normal direction of the array element and the x axis is shown; Δ d mn The circumferential position error of the array element is obtained; Δ z mn Is the axial position error of the array element;
(12b) According to the directional diagram of the cylindrical conformal array antenna, the electrical properties such as a first minor lobe level SLL, beam pointing BP and the like are obtained;
(12c) Based on the design index gain loss of the antenna being less than 0.5dB, the electrical performance deterioration degree of the antenna side lobe level rise quantity delta SLL and the beam pointing deviation delta BP is calculated.
The step (13) of increasing the elastic modulus of the cylindrical conformal array antenna structure includes the following steps: increasing the elastic modulus, for example, making the elastic modulus take values (unit: gpa) respectively according to the following sequence:
[10,20,30,40,50,60,70,80,90,100,110]。
compared with the prior art, the invention has the following characteristics:
1. the established electromechanical coupling model of the cylindrical conformal array antenna is utilized to realize accurate mapping between structural parameters and electrical properties of the cylindrical conformal array antenna, the optimal elastic modulus of the cylindrical conformal array antenna structure can be rapidly calculated, the electrical properties of the cylindrical conformal array antenna under different frequency bands can be analyzed, and the cylindrical conformal array antenna has good applicability.
2. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure is constructed, so that the elastic modulus can be gradually increased to calculate the electrical property calculation of the deformed cylindrical conformal array antenna, the calculation result is compared with the design index requirement, the rationality of the structural scheme of the cylindrical conformal array antenna can be judged, the defects that the design is carried out by experience and the design scheme is repeatedly modified by processing the actual measurement electrical property of a sample piece are overcome, the development period is shortened, and the development cost is reduced.
Drawings
FIG. 1 is a flow chart of a method for determining an optimal elastic modulus of a cylindrical conformal array antenna structure based on electromechanical coupling according to the present invention;
FIG. 2 is a schematic diagram of the element arrangement of a cylindrical conformal array antenna;
FIG. 3 is a schematic diagram showing the relationship between the rectangular array coordinate system and the rectangular array coordinate system;
FIG. 4 is a schematic diagram showing the relationship between an array element rectangular coordinate system and an array element spherical coordinate system;
FIG. 5 is a schematic view of a target spatial geometry;
FIG. 6 is a schematic diagram of a cylindrical conformal array antenna structure;
FIG. 7 is a grid model of a cylindrical conformal array antenna in ANSYS software;
FIG. 8 is a schematic diagram of constrained positions of a cylindrical conformal array antenna model;
fig. 9 is a displacement cloud of a cylindrical conformal array antenna;
fig. 10 is an antenna radiation pattern with and without loading for a cylindrical conformal array antenna;
fig. 11 is an antenna radiation pattern for different elastic moduli of a cylindrical conformal array antenna;
FIG. 12 is a graph of gain loss versus load magnitude;
fig. 13 is a graph of maximum side lobe level variation versus load size.
Detailed Description
The invention is further described in detail below with reference to the drawings and examples, but the invention is not limited thereto.
As shown in fig. 1, the method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling specifically includes the following steps:
step 1, determining structural parameters and electromagnetic parameters of the cylindrical conformal array antenna.
1.1 determining the cylinder radius r of the cylinder conformal array antenna, the circumferential row number M and the axial column number N of the array elements in the array, the circumferential central angle gamma and the axial distance d of the adjacent array elements z (see fig. 2), and the structural parameters and the operating frequency f of the array elements;
1.2 numbering array elements in the array surface according to the sequence of circumferential rows and axial columns as (M, N), wherein M is an integer between 1 and M and represents the number of the Mth row of array elements of the cylindrical conformal array antenna, and N is an integer between 1 and N and represents the number of the Nth row of array elements of the cylindrical conformal array antenna.
And 2, giving the elastic modulus of the initial cylindrical conformal array antenna structure.
And determining the elastic modulus of the initial cylindrical conformal array antenna structure according to the actual working condition of the cylindrical conformal array.
And 3, performing structural load deformation analysis on the cylindrical conformal array antenna by using mechanical analysis software, wherein the structural load comprises a vibration load and a thermal load.
And according to the load borne by the cylindrical conformal array, performing structural load deformation analysis on the cylindrical conformal array antenna by using mechanical analysis software.
And 4, obtaining the circumferential and axial position offset of each array element based on the structural load deformation analysis result of the cylindrical conformal array antenna, and solving the new position of the deformed array element.
4.1 obtaining the circumferential position offset delta d of each array element according to the result of the load deformation analysis of the cylindrical conformal array antenna structure in the step (3) mn And the amount of axial position deviation Δ z mn 。
4.2 setting the design coordinates of (m, n) array elements in the array as (x) mn ,y mn ,z mn ) The included angle between the local external normal direction of the array element and the x axis is gamma mn Wherein x is mn ＝r·cosγ mn ，y mn ＝r·sinγ mn And then, the following steps are known:
wherein r is the radius of the cylinder;
4.3 circumferential position offset Δ d of Combined array elements mn And the amount of axial position deviation Δ z mn Circumferential arc length Δ d mn Corresponding to a central angle ofThe new position (x ') of the deformed array element can be known' mn ,y′ mn ,z′ mn )：
And 5, establishing a rectangular array element coordinate system and a spherical array element coordinate system according to the new position of the deformed array element.
5.1. According to the deformationEstablishing a rectangular coordinate system of the array elements according to the new positions of the array elementsO′ mn Is the phase center of the (m, n) th array element after deformation,the positive direction of the axis is the local external normal direction of the curved surface placed by the array element after deformation,the axis is in the same direction as the z-axis,tangent to the plane of the antenna element;
5.2. according to the established rectangular array element coordinate system, an array element spherical coordinate system is establishedWhereinPositive direction is O mn ' a radial direction pointing to any point,the far field direction of the deformed array element coordinate system;in the positive direction ofThe shaft looks downwardsThe shaft being rotated anticlockwise to the sagittal diameterThe tangential direction of the projection of the surface,in the positive direction ofThe shaft rotates clockwise to the tangent of the sagittal diameter.
And 6, determining a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system.
According to the transformation relation between the spherical coordinate system and the rectangular coordinate system, the array element spherical coordinate system can be obtainedDirection vector to array element rectangular coordinate systemThe conversion matrix of (2):
in the formula (I), the compound is shown in the specification,and the matrix is a conversion matrix from the array element spherical coordinate system to the array element rectangular coordinate system.
And 7, based on the array element directional diagram in the array element spherical coordinate system, solving the array element directional diagram in the array element rectangular coordinate system by using a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system.
7.1 according to the array element structure parameters, obtaining the directional diagram of the deformed array element under the array element spherical coordinate system:
in the formula (I), the compound is shown in the specification,andin an array element spherical coordinate system for an array element directional diagramAnda component of direction;
7.2 Combined array element spherical coordinate systemAnd array element rectangular coordinate system direction vectorIs converted into a matrixAnd the directional diagram of the deformed array element under the array element spherical coordinate system can obtain the array element directional diagram of the array element under the array element rectangular coordinate system:
in the formula (I), the compound is shown in the specification,andarray element rectangular coordinate system respectively for array element directional diagramAndthe component of the direction.
And 8, determining a conversion matrix of the rectangular coordinate system of the array elements and the rectangular coordinate system of the array according to the new positions of the deformed array elements.
According to the new position of the deformed array element, a conversion matrix from the rectangular array element coordinate system to the rectangular array coordinate system can be determined:
in the formula (I), the compound is shown in the specification,and converting the deformed array element rectangular coordinate system into an array rectangular coordinate system.
And 9, based on the array element directional diagram under the array element rectangular coordinate system, solving the array element directional diagram under the array rectangular coordinate system by using the conversion matrix of the array element rectangular coordinate system and the array rectangular coordinate system.
9.1 through the transformed array element rectangular coordinate system to the conversion matrix T 'of the array rectangular coordinate system' eta (Δd mn ) Obtaining far field direction of the deformed array element coordinate systemThe relation between the far field direction (theta, phi) and the array coordinate system;
one point in the far field is represented in the rectangular array coordinate system as:
the point is expressed as follows in the rectangular array element coordinate system:
distance of point in far zone field to origin of local coordinate system of array elementEqual to its distance R from the origin of the array coordinate system, so there are:
thereby can obtainDetermining the far field directions (theta, phi) in the array coordinate system and the far field directions in the array element coordinate systemThe relationship between;
9.2 combining the array element directional diagram under the array element rectangular coordinate system, converting the transformed array element rectangular coordinate system to a conversion matrix T 'of the array rectangular coordinate system' eta (Δd mn ) And obtaining an array element directional diagram of the deformed array element under the array rectangular coordinate system:
in the formula (f) mnx (θ,φ,Δd mn )、f mny (θ,φ,Δd mn ) And f mnz (θ,φ,Δd mn ) The components of the deformed array element direction diagram in the three directions of an array rectangular coordinate system x, y and z are respectively; t' eta (Δd mn ) The transformation matrix is a transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;the unit vectors are respectively in three directions of an array rectangular coordinate system x, y and z.
And step 10, determining the excitation amplitude and phase of the array elements according to the orofacial weighted distribution.
And determining the excitation amplitude and phase of the array elements according to the weighted distribution of the oral surface.
And step 11, calculating the spatial phase difference of each array element at the target position by combining the position of the phase reference point of the cylindrical conformal array antenna and the new position of the deformed array element.
11.1 Unit vector of phase reference point O to any point P (x, y, z) in far field
In the formula (I), the compound is shown in the specification,the unit vectors are respectively in three directions of an array rectangular coordinate system x, y and z.
11.2 according to the new position of the (m, n) th array element after deformation, a unit vector relative to the origin O of the coordinate system can be obtained:
11.3, the space phase difference of the deformed array elements at the target is as follows:
in the formula (I), the compound is shown in the specification,is a phase reference point O to the far fieldMeaning the unit vector of the point P (x, y, z) direction,the unit vector of the position of the deformed array element relative to the origin O of the coordinate system; r is the radius of the cylinder; (x) mn ,y mn ,z mn ) And designing coordinates for the array elements.
Step 12, calculating a directional diagram of the cylindrical conformal array antenna under the action of the load by using an electric coupling model of the cylindrical conformal array antenna; and calculating the electrical property parameters of the antenna according to the directional diagram of the cylindrical conformal array antenna, and analyzing the deterioration degree of the electrical property relative to the design index of the cylindrical conformal array antenna.
12.1, calculating a directional diagram of the deformed cylindrical conformal array antenna by using an electromechanical coupling model of the cylindrical conformal array antenna:
in the formula:
I mn for the purpose of its energizing of the current,respectively the amplitude and the phase of the exciting current;
a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system;
T′ eta (Δd mn ) A transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;
the directional diagrams of the deformed array elements under the rectangular coordinate systems of the array elements are the same;
the spatial phase difference of the deformed array elements at the target can be expressed as:r is the radius of the cylinder; gamma ray mn The included angle between the local external normal direction of the array element and the x axis is shown; Δ d mn The circumferential position error of the array element is obtained; Δ z mn The axial position error of the array element is obtained;
12.2 obtaining electrical properties such as a first minor lobe level SLL and a beam pointing BP according to a cylindrical conformal array antenna directional diagram;
12.3 based on the design index of the antenna, the gain loss is less than 0.5dB, and the electrical property deterioration degree of the antenna side lobe level rise quantity delta SLL and the beam pointing deviation delta BP is calculated.
And step 13, judging whether the calculated electrical property parameters meet the requirements or not according to the antenna design requirements.
Judging whether the electrical property of the cylindrical conformal array antenna under the elastic modulus condition meets the requirement or not according to the design index requirement of the cylindrical conformal array antenna, wherein if the electrical property meets the requirement, the current elastic modulus is the optimal elastic modulus of the cylindrical conformal array antenna structure; otherwise, increasing the elastic modulus, and repeating the steps (2) to (12) until the electrical performance of the cylindrical conformal array antenna meets the requirement.
Increasing the elastic modulus, for example, making the elastic modulus take values (unit: gpa) according to the following sequence:
[10,20,30,40,50,60,70,80,90,100,110]。
the advantages of the present invention can be further illustrated by the following simulation experiments:
1. simulation conditions
The cylindrical conformal array antenna with the central working frequency of 3GHz and the array elements of the half-wave dipole antenna is taken as an example. As shown in tables 1-3, the radius of 995mm at the inner surface of the cylindrical support layer, the radius of 1000mm at the outer surface of the cylindrical support layer, the height of the cylinder, and the height of the cylinder correspond to those of the cylindrical surfaceThe central angle was 25.2 °. The number of rows and columns of array elements along the circumferential direction and the axial direction of the cylinder is M =3, N =5, the circumferential distance d of adjacent array elements is =0.8 lambda, and the axial distance d of adjacent array elements is z =0.5 λ. And selecting the gain loss less than 0.5dB as an electrical performance index of the cylindrical conformal array antenna.
TABLE 1 geometric model parameters for cylindrical conformal array antennas
TABLE 2 Material Properties for cylindrical conformal array antennas
TABLE 3 electromagnetic operating parameters of cylindrical conformal array antennas
2. Calculating the electrical performance of the cylindrical conformal array antenna under the current structural parameters
1. Establishing a finite element model of a cylindrical conformal array antenna structure
And establishing a structural finite element model of the cylindrical conformal array antenna in ANSYS software according to the geometric model size and the material property parameters of the cylindrical conformal array antenna, as shown in FIG. 6. According to the engineering practice, the material properties of carrier layers such as an antenna array surface frame and a mounting bracket are set according to the material parameters of aluminum alloy in the table 2, and the material properties of array elements are set according to the material parameters of copper. The carrier layer unit type and the antenna array element type are all SOLID units SOLID185, and the carrier layer and the array element are connected with each other through a connecting piece. The geometric structure model of the cylindrical conformal array antenna is subjected to grid division by using a free grid set by ANSYS software, and a grid model of the cylindrical conformal array antenna is obtained as shown in FIG. 7.
2. Applying constraint and load to obtain the circumferential and axial position deviation of each array element
2.1 according to the installation position of the support in engineering practice, adopting cantilever beam structure stress analysis, fixing one end of the cylindrical conformal array antenna as a constraint condition as shown in fig. 8, and according to the constraint condition of a finite element model of the cylindrical array antenna and the given uniformly distributed load, F =100N. (ii) a
2.2, carrying out load deformation analysis on the cylindrical conformal array antenna by using ANSYS software to obtain the deformation of each node of the cylindrical conformal array antenna, drawing a displacement cloud chart of the cylindrical conformal array antenna, as shown in FIG. 9, and obtaining the position offset of each array element. And extracting a finite element model of each array element of the cylindrical conformal array antenna, and acquiring the circumferential and axial position offset of each array element.
3. Calculating the directional pattern of a cylindrical conformal array antenna
According to the following equations (3), (4), (7), (15), and (12), the directional diagram function of the cylindrical conformal array antenna is obtained by establishing an array rectangular coordinate system, and an array element spherical coordinate system of the cylindrical conformal array antenna according to fig. 3 and 4, and according to the equations (3), (4), (7), and (15), and by combining the target space geometric relationship shown in fig. 5:
in the formula:
I mn for the purpose of its energizing of the current,respectively the amplitude and the phase of the exciting current;
a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system is formed;
T′ eta (Δd mn ) For the transformed matrix from the array element rectangular coordinate system to the array rectangular coordinate system；
In order to obtain a directional diagram of the deformed array elements under the rectangular coordinate system of the array elements, the directional diagram of each deformed array element under the rectangular coordinate system of the array element is the same under the assumption that the structure of the array element is not changed under the load environment;
the spatial phase difference of the deformed array elements at the target can be expressed as:r is the radius of the cylinder; gamma ray mn The included angle between the local external normal direction of the array element and the x axis is shown; Δ d mn The circumferential position offset of the array element is taken as the offset; Δ z mn Is the axial position offset of the array element.
3. Simulation results and analysis
1. Under the action of the uniformly distributed load of 100N, the maximum node displacement of the cylindrical conformal antenna can be seen to be 2.53146mm, and the maximum node displacement appears at the position of the most edge of the antenna structure. Substituting the obtained position offset of the array element into the electric coupling model of the cylindrical conformal antenna to calculate the radiation pattern of the cylindrical conformal array antenna, as shown in fig. 10. It can be known that under the load, the gain of the cylindrical conformal array antenna is reduced by 0.7838dB (> gain loss is 0.5 dB), the maximum side lobe level is raised by 3.09dB, and the performance of the cylindrical conformal array antenna does not meet the requirement.
2. The elastic modulus of the cylindrical conformal array antenna carrier layer is selected as the structural parameter needing to be optimized, the elastic modulus of the antenna carrier layer is modified, and the electrical property of the cylindrical conformal array antenna is calculated. The radiation patterns of the cylindrical conformal array antenna when the carrier layer elastic modulus is 70GPa, 71GPa, 72GPa, 73GPa, 74GPa, 75GPa, 76GPa, 77GPa, 78GPa, 79GPa, 80GPa, 81GPa, 82GPa, 83GPa are shown in fig. 11, the antenna electrical performance parameters are shown in table 4, and the gain variation and the maximum secondary lobe level variation under different carrier layer elastic moduli are shown in fig. 12 and 13, respectively.
TABLE 4 comparison table of electrical property parameters of antenna under different elastic moduli
Note: the maximum side lobe level in the table refers to the difference between the larger of the left and right side lobe levels and the main lobe
For this cylindrical conformal array antenna, analysis of fig. 10, 11, 12, 13 and table 4 can see that: (1) The gain of the cylindrical conformal array antenna is reduced under the action of load, and the maximum side lobe level is raised; (2) The gain loss of the cylindrical conformal array antenna is gradually reduced along with the continuous increase of the elastic modulus of the antenna carrier layer; (3) The maximum side lobe level variation of the cylindrical conformal array antenna is gradually reduced along with the increase of the elastic modulus of the carrier layer; (4) When the elastic modulus of the cylindrical conformal array antenna carrier layer is increased to 81GPa, the antenna gain loss is 0.4904dB (< gain loss 0.5 dB), the maximum side lobe level is raised by 1.27dB, the electrical performance requirement of the cylindrical conformal array antenna under a load environment is met, the elastic modulus of the optimized cylindrical conformal array antenna carrier layer is 81Gpa, and the optimized antenna structure parameters are determined.
The simulation numerical experiment proves that the optimal elastic modulus of the cylindrical conformal array antenna structure can be effectively determined, the electromechanical coupling model of the cylindrical conformal array antenna can be used for calculating the electrical property of the cylindrical conformal array antenna under the current elastic modulus condition, and when the performance index of the antenna does not meet the requirement, the optimal elastic modulus of the cylindrical conformal array antenna structure can be effectively determined by using the electromechanical coupling model, so that the optimal elastic modulus of the cylindrical conformal array antenna structure meeting the requirement of the antenna performance index is obtained.
Claims (10)
1. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling is characterized by comprising the following steps of:
(1) Determining structural parameters and electromagnetic parameters of the cylindrical conformal array antenna according to a structural design scheme of the cylindrical conformal array antenna;
(2) The elastic modulus of an initial cylindrical conformal array antenna structure is given;
(3) According to the antenna load environment, performing load deformation analysis on the cylindrical conformal array antenna by using mechanical analysis software ANSYS;
(4) Based on the result of structural load deformation analysis of the cylindrical conformal array antenna, obtaining the circumferential and axial position offset of each array element, and solving the new position of the deformed array element;
(5) According to the new position of the deformed array element, establishing an array element rectangular coordinate system and an array element spherical coordinate system;
(6) Determining a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system;
(7) Based on an array element directional diagram under an array element spherical coordinate system, a conversion matrix between the array element rectangular coordinate system and the array element spherical coordinate system is utilized to obtain the array element directional diagram under the array element rectangular coordinate system;
(8) Determining a conversion matrix of the rectangular coordinate system of the array elements and the rectangular coordinate system of the array according to the new positions of the deformed array elements;
(9) Based on the array element directional diagram under the array element rectangular coordinate system, the array element directional diagram under the array element rectangular coordinate system is solved by utilizing the conversion matrix of the array element rectangular coordinate system and the array rectangular coordinate system;
(10) Determining array element excitation amplitude and phase according to the orofacial weighted distribution;
(11) Calculating the spatial phase difference of each array element at the target position by combining the position of the phase reference point of the cylindrical conformal array antenna and the new position of the deformed array element;
(12) Calculating a directional diagram of the cylindrical conformal array antenna under the elastic modulus condition by utilizing an electric coupling model of the cylindrical conformal array antenna; calculating electrical property parameters of the antenna according to a directional diagram of the cylindrical conformal array antenna, and analyzing the deterioration degree of the electrical property relative to the design index of the cylindrical conformal array antenna;
(13) According to the design index requirement of the cylindrical conformal array antenna, the gain loss is less than 0.5dB, whether the electrical property of the cylindrical conformal array antenna under the elastic modulus condition meets the requirement is judged, and if the electrical property meets the requirement, the current elastic modulus is the optimal parameter of the cylindrical conformal array antenna structure; otherwise, increasing the elastic modulus, and repeating the steps (2) to (12) until the electrical property of the cylindrical conformal array antenna meets the requirement.
2. The method for determining the optimal elastic modulus of the cylinder conformal array antenna structure based on electromechanical coupling according to claim 1, wherein the step (1) is performed according to the following procedures:
(1a) Determining the cylinder radius r of the cylinder conformal array antenna, the circumferential row number M and the axial column number N of the array elements in the array, the circumferential central angle gamma and the axial distance d of the adjacent array elements z And the structural parameters and the working frequency f of the array elements;
(1b) And numbering array elements in the array surface into (M, N) according to the sequence of circumferential rows and axial columns, wherein M is an integer between 1 and M and represents the number of the Mth row of array elements of the cylindrical conformal array antenna, and N is an integer between 1 and N and represents the number of the Nth column of array elements of the cylindrical conformal array antenna.
3. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 1, wherein the step (4) is performed as follows:
(4a) Obtaining the circumferential position offset delta d of each array element according to the result of the load deformation analysis of the cylindrical conformal array antenna structure in the step (3) mn And the amount of axial position deviation Δ z mn ；
(4b) Setting the design coordinates of (m, n) array elements in the array as (x) mn ,y mn ,z mn ) The included angle between the local external normal direction of the array element and the x axis is gamma mn Wherein x is mn ＝r·cosγ mn ，y mn ＝r·sinγ mn Thus, it can be seen that:
wherein r is the radius of the cylinder;
(4c) Combined with circumferential position offset deltad of array element mn And the amount of axial position deviation Δ z mn Circumferential arc length Δ d mn Corresponding central angle ofThe new position (x ') of the deformed array element can be known' mn ,y′ mn ,z′ mn )：
4. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 1, wherein the step (5) is performed as follows:
(5a) Establishing an array element rectangular coordinate system according to the new position of the deformed array elementO′ mn Is the phase center of the (m, n) th array element after deformation,the positive direction of the axis is the local external normal direction of the curved surface placed by the array element after deformation,the axis is in the same direction as the z-axis,tangent to the plane of the antenna element;
(5b) According to the established rectangular array element coordinate system, an array element spherical coordinate system is establishedWhereinIn the positive direction of O mn ' a radial direction pointing to any point,the far field direction of the deformed array element coordinate system is shown;in the positive direction ofThe shaft looks downwardsThe shaft being rotated anticlockwise to the sagittal diameterThe tangential direction of the projection of the surface,in the positive direction ofThe shaft rotates clockwise to the tangent of the sagittal diameter.
5. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 4, wherein the step (6) is performed as follows:
according to the transformation relation between the spherical coordinate system and the rectangular coordinate system, the array element spherical coordinate system can be obtainedArrival matrixDirection vector of rectangular coordinate systemThe transformation matrix of (2):
in the formula (I), the compound is shown in the specification,the matrix is a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system.
6. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 4, wherein the step (7) is performed as follows:
(7a) According to the array element structure parameters, the directional diagram of the deformed array element under the array element spherical coordinate system can be obtained:
in the formula (I), the compound is shown in the specification,andin an array element spherical coordinate system for an array element directional diagramAnda component of direction;
(7b) Combined array element spherical coordinate systemAnd array element rectangular coordinate system direction vectorOf the conversion matrixAnd the deformed array element directional diagram under the array element spherical coordinate system can obtain the array element directional diagram under the array element rectangular coordinate system:
in the formula (I), the compound is shown in the specification,andarray element rectangular coordinate system respectively for array element directional diagramAndthe component of the direction.
7. The method for determining the optimal elastic modulus of the cylinder conformal array antenna structure based on electromechanical coupling according to claim 1, wherein the step (8) is performed according to the following procedures:
according to the new position of the deformed array element, a conversion matrix from the rectangular array element coordinate system to the rectangular array coordinate system can be determined:
in the formula (II), T' eta (Δd mn ) And converting the transformed array element rectangular coordinate system into an array rectangular coordinate system.
8. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 6, wherein the step (9) is performed as follows:
(9a) Converting matrix T 'from transformed array element rectangular coordinate system to array rectangular coordinate system' eta (Δd mn ) Obtaining the far field direction of the deformed array element coordinate systemThe relation between the far field direction (theta, phi) and the array coordinate system;
one point in the far field is represented in the rectangular array coordinate system as:
x＝R sinθcosφ
y＝R sinθsinφ
z＝R cosθ
the point is expressed as follows in the rectangular array element coordinate system:
distance from point in far field to origin of local coordinate system of array elementEqual to its distance R from the origin of the array coordinate system, so there are:
thereby can obtainDetermining the far field directions (theta, phi) in the array coordinate system and the far field directions in the array element coordinate systemThe relationship between them;
(9b) Combining the array element directional diagram under the array element rectangular coordinate system, and converting the transformed array element rectangular coordinate system to the array rectangular coordinate system to obtain a matrix T' eta (Δd mn ) And obtaining an array element directional diagram of the deformed array elements under the array rectangular coordinate system:
in the formula (f) mnx (θ,φ,Δd mn )、f mny (θ,φ,Δd mn ) And f mnz (θ,φ,Δd mn ) The components of the deformed array element directional diagram in three directions of an array rectangular coordinate system x, y and z are respectively; t' eta (Δd mn ) A transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;is a unit vector of three directions of x, y and z of an array rectangular coordinate system respectively。
9. The method for determining the optimal elastic modulus of the cylinder conformal array antenna structure based on electromechanical coupling as claimed in claim 1, wherein the step (11) is performed according to the following procedures:
(11a) Unit vector of phase reference point O to any point P (x, y, z) direction of far field
In the formula (I), the compound is shown in the specification,the unit vectors are respectively in the x direction, the y direction and the z direction of the rectangular array coordinate system;
(11b) From the new position of the (m, n) -th array element after the transformation, the unit vector of the (m, n) -th array element relative to the origin O of the coordinate system can be obtained:
wherein r is the radius of the cylinder; gamma ray mn The included angle between the local external normal direction of the array element and the x axis is shown; Δ d mn The circumferential position offset of the array element is taken as the offset; Δ z mn The axial position offset of the array element is taken as the axial position offset of the array element;
(11c) The space phase difference of the deformed array elements at the target position is as follows:
in the formula (I), the compound is shown in the specification,is far from phase reference point OThe unit vector of any point P (x, y, z) direction of the field,the unit vector of the position of the deformed array element relative to the origin O of the coordinate system; r is the radius of the cylinder; (x) mn ,y mn ,z mn ) And designing coordinates for the array elements.
10. The method for determining the optimal elastic modulus of the cylindrical conformal array antenna structure based on electromechanical coupling according to claim 1, wherein the step (12) is performed as follows:
(12a) Calculating a directional diagram of the deformed cylindrical conformal array antenna by using an electric coupling model of the cylindrical conformal array antenna:
in the formula:
I mn for the purpose of its energizing of the current,A mn ，respectively the amplitude and the phase of the exciting current;
a conversion matrix from an array element spherical coordinate system to an array element rectangular coordinate system is formed;
T′ eta (Δd mn ) A transformation matrix from the deformed array element rectangular coordinate system to the array rectangular coordinate system;
the deformed array elements are at right angles to the array elementsDirectional diagrams under the coordinate system are the same in the directional diagrams of the array elements after each deformation under the rectangular coordinate system of the array elements;
the spatial phase difference of the deformed array elements at the target can be expressed as:r is the radius of the cylinder; gamma ray mn The included angle between the local external normal direction of the array element and the x axis is shown; Δ d of mn The circumferential position error of the array element is obtained; Δ z mn The axial position error of the array element is obtained;
(12b) Obtaining a first minor lobe level SLL according to a cylindrical conformal array antenna directional diagram, wherein a beam points to BP electrical property;
(12c) Based on the design index gain loss of the antenna being less than 0.5dB, the electrical performance deterioration degree of the antenna side lobe level rise quantity delta SLL and the beam pointing deviation delta BP is calculated.
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| CN113378441A (en) * | 2021-06-28 | 2021-09-10 | 上海东峻信息科技有限公司 | Delay construction method of deformable surface bound conformal array unit |
| CN115034075A (en) * | 2022-06-22 | 2022-09-09 | 电子科技大学 | Rapid and accurate prediction method for irregular antenna array vector gain directional diagram |
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| CN113378441A (en) * | 2021-06-28 | 2021-09-10 | 上海东峻信息科技有限公司 | Delay construction method of deformable surface bound conformal array unit |
| CN113378441B (en) * | 2021-06-28 | 2023-11-10 | 上海东峻信息科技有限公司 | Delay construction method of conformal array unit with deformable surface constraint |
| CN115034075A (en) * | 2022-06-22 | 2022-09-09 | 电子科技大学 | Rapid and accurate prediction method for irregular antenna array vector gain directional diagram |
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